Newton—Riemann时空中的动力学（Ⅲ）

讨论了Newton-Riemann时空中的动力学－－Hamilton力学及其在流体力学中的应用。     

Newton—Riemann时空中的动力学（Ⅱ）

讨论了Newton-Riemann时空中运动的相对性及运动方程的协变性,N－R时空中Newton力学与广义相对论的某些关系及其异同。     

一维非线性弹性力学方程组的Riemann问题

本文研究了一维非线性弹性力学方程组的Riemann问题.根据左右状态所处的相对位置,分情况构造了问题的唯一整体解.由于激波条件退化,系统的基本波除了稀疏波和激波还包含退化激波.     

Newtonian-Riemannian时空中的动力学(Ⅰ)

根据现代微分几何的理论,力学原理及现代微积分把Newtonian-Galilean时空中的动力学推广到Newtonian-Riemannian时空中,建立N-R时空中的动力学,分几个部分,(Ⅰ)是其中之一,余后续。     

Ne wtonian-Rie mannian时空中的动力学(Ⅰ)

根据现代微分几何的理论 ,力学原理及现代微积分把Newtonian_Galilean时空中的动力学推广到Newtonian_Riemannian时空中 ,建立N_R时空中的动力学 ,分几个部分 ,(Ⅰ )是其中之一 ,余后续·     

滑冰运动初探

建立了滑冰运动的一种力学模型并应用非完整力学中的Routh方程对其求解。详细分析了滑冰时的两种局部有意义的常见的定常运动,计算结果与实际观察到的现象是一致的。     

《应用数学和力学》投稿指南北大核心CSCD

1．我刊主要刊登力学、力学中的数学方法和与现代力学紧密相关的应用数学方面的高水平学术论文,同时刊登土木建筑、水利水工、道路桥梁、航海造船、航空航天、机械冶金、国防军工、防灾减灾、能源环保、生物化工等领域中力学和数学建模、分析方面具有学术水平和实用价值的论文。来稿务求观点明确、论据可靠、数字准确、文字精练,推导从简,给出主要成果和结论。     

力学中单参数变换群的应用

本文包括无限小形式的变换群用于减少偏微分方程中的自变量,获得相似变量的理论,以及它在力学中具有两个自变量、两个因变量的非线性偏微分方程组中的应用。     

三维非局部弹性场中裂纹问题的分析方法

通过求解得到了三维非局部弹性力学对称情形的单位集中不连续位移基本解·基于该基本解和三维局部（经典）弹性力学的不连续位移边界积分方程———边界元方法·提出了三维非局部弹性力学中的平片裂纹Ⅰ型问题的通用解法,并给出了算例     

Riemann问题的间断有限元

用时空全离散间断零次有限元对Riemarm问题进行了数值求解，没有出现振荡，很好的模拟了稀疏波的逐渐稀疏化和激波的剧烈变化。     

双曲型Lagrangian函数*

双曲复数与Minkowski几何相对应,由四维时空间隔不变量和双曲型Lorentz变换可导出双曲型Lagrangian方程和Hamilton-Jacobi方程.     

流体动力学的客观性要求

从流体动力学的客观性要求导出了新的流动理论.流动运动的不均匀性产生粘性力,不同观察者的选取会影响这种不均匀分布特征.将粘性力看作一种与观察者的选取无关的客观存在时,粘性力和动量方程在局域旋转变换下的形式不变性要求引入一种新的动力学场——涡旋场,通过构造流体系统的拉朗日密度并利用能量变分方法得到了所有场量的动力学方程.     

Kahler流形上的Lagrange向量场*

本文中。我们讨论K?hler流形上的Lagrange向量场,并用它来描述和解决Khler流形上的Newton力学和Lagrange力学中的一些问题。     

K(a)hler流形上的不变形式和积分不变量

用现代微分几何理论和高等微积分把Poincare和Cartan-Poincare积分不变量的晕要思想和结果以及E．Cartan在经典力学中首先建立的积分不变量和不变形式的关系推广到Kahler流形上的Hamilton力学中去，得到相应的更广泛的结果．     

On a Deformation-Driven Continuum-Related Parrinello-Rahman Molecular Dynamics

Investigations into the atomistic-to-continuum coupling are recently pursued in literature. A hierarchical modelling in terms of a macroscale treated by continuum mechanics and the microscale governed by statistical mechanics may be a very fruitful combination. If the microscale is simulated with the help of molecular dynamics, the isostress-isoenthalpic ensemble as proposed by Parrinello and Rahman presents a beneficial choice. This statistical ensemble is remarkable as the equations of motion are derived from a Lagrangian. Recently, this Lagrangian was situated into a continuum mechanics setting. This paper investigates the behavior of this continuum-related Lagrangian in a kinetics-driven setting (by imposing an external stress) and a kinematics-driven setting (by imposing the shape of the molecular dynamics cell) in terms of a numerical example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational and Geometric Structures of Discrete Dirac Mechanics

In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew’s triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete Lagrange–Dirac and nonholonomic Hamiltonian systems. In particular, this yields nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange–d’Alembert–Pontryagin and Hamilton–d’Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics, as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.     

Singularities of Lagrangian varieties and related topics

We study the classification problem for generic projections of Lagrangian submanifolds. A classification list for symmetric Lagrangian submanifolds is obtained and the generic evolutions of symmetric caustics are illustrated. We show how the singular Lagrangian varieties appear in the invariant theory of binary forms and we introduce the basic concepts of the desingularization procedure. Applications to differential geometry, geometrical optics, and mechanics are presented.